There was a discussion of this a few weeks ago on the mailinglist of a scientific software project I use. The people were very clearly divided into the "Flash does it, so it's ok" and "omg no, think of the user privacy" camps, it was quite interesting.
I think I'm much more ok with background things upgrading in the background. For instance: I never open a new browser tab and think "hmmm, lets launch a Flash process", it's just there, ready to respond when needed. So it isn't shocking to find that it polls for updates and applies them.
By contrast, git is a tool that I manually invoke on the command line, and when the process terminates it's done. Having that phone home at runtime feels more invasive.
A tool printing "This version has a critical vulnerability, upgrade immediately" wouldn't be confusing though, or cause any problems. Even if it wasn't connected to the network, it simply wouldn't print that message. Everything else would still work properly.
It seems like people are worried about privacy without thinking it through.
